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Maximum packings of the \(\lambda\)-fold complete 3-uniform hypergraph with loose 3-cycles. (English) Zbl 1437.05191

Summary: It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order \(v\) if and only if \(v \equiv 0, 1,\text{ or }2\pmod 9\). For all positive integers \(\lambda\) and \(v\), we find a maximum packing with loose 3-cycles of the \(\lambda\)-fold complete 3-uniform hypergraph of order \(v\). We show that, if \(v \geq 6\), such a packing has a leave of two or fewer edges.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C35 Extremal problems in graph theory
05C65 Hypergraphs
05C85 Graph algorithms (graph-theoretic aspects)
05C38 Paths and cycles
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